Transmission and reception system with guard intervals containing known components unrelated to transmitted data

ABSTRACT

A receiver receives a signal containing data distributed in both time and frequency. The receiver includes a vector transform arranged to perform a transform on the received signal using a plurality of receiver transform vectors. The receiver transform vectors are based upon a corresponding plurality of transmitter vectors modified in accordance with channel effects so that the data can be recovered by the vector transform even in the presence of strong ghosts.

TECHNICAL FIELD OF THE INVENTION

[0001] The present invention is directed to an equalizer thatsubstantially eliminates ghosts in signals processed by a receiver.

BACKGROUND OF THE INVENTION

[0002] Ghosts are produced in a receiver usually because a signalarrives at the receiver through different transmission paths. Forexample, in a system having a single transmitter, the multipathtransmission of a signal may occur because of signal reflection. Thatis, the receiver receives a transmitted signal and one or morereflections of the transmitted signal. As another example, the multipathtransmission of a signal may occur in a system having pluraltransmitters that transmit signals to the same receiver using the samecarrier frequency. A network which supports this type of transmission istypically referred to as a single frequency network.

[0003] When a signal reaches a receiver through two or more differenttransmission paths, an interference pattern results. In the frequencydomain, this interference pattern is manifested by a variable signalamplitude along the frequency axis. The worst case interference patternresults when the ghost is 100% and is shown in FIG. 1. This interferencepattern has amplitude nulls or near amplitude nulls at certainfrequencies. Therefore, any information contained in the received signalat these frequencies is likely lost because the signal to noise rationear these frequencies is below a usable threshold.

[0004] A variety of systems have been devised to deal with the problemscaused by ghosts. For example, spread spectrum systems deal veryadequately with the problem of a 100% ghost by spreading the transmitteddata over substantial bandwidth. Accordingly, even though a 100% ghostmeans that some information may be lost at the frequencies correspondingto amplitude nulls, a data element can still be recovered because of thehigh probability that it was spread over frequencies which do notcorrespond to amplitude nulls. Unfortunately, the data rate R associatedwith spread spectrum systems is typically too low for many applications.(The data rate R is defined as the number of data bits per Hertz ofchannel bandwidth.)

[0005] It is also known to use a matched filter in a receiver in orderto deal with the problem of a ghost. In this approach, data istransmitted as a data vector. The matched filter correlates the receiveddata with reference vectors corresponding to the possible data vectorsthat can be transmitted. Correlation of the received signal to thereference vector corresponding to the transmitted data vector produces alarge peak, and correlation of the received signal to the other possiblereference vectors produces small peaks. Accordingly, the transmitteddata vector can be easily determined in the receiver. Unfortunately, thedata rate R typically associated with the use of matched filters isstill too low for many applications.

[0006] When high data rates, such as R≧1, are required, equalizers areoften used in a receiver in order to reduce ghosts. A classic example ofa time domain equalizer is an FIR filter. An FIR filter convolves itsresponse h(t), shown generally in FIG. 2, with the received signal andproduces a large peak representative of the main received signal. Ghostshave small components in the output of the FIR filter. However, as shownin FIG. 2, the values a a², a³, . . . of the taps of an FIR filterdepend on the value of a and, in order to perfectly cancel a 100% ghostusing an FIR filter, the value a of the FIR filter response mustapproach 1. As the value a approaches 1, the values of the taps of theFIR filter do not asymptotically decrease toward zero. Therefore, theFIR filter becomes infinitely long if a 100% ghost is to be eliminated,making the FIR filter impractical to eliminate a 100% ghost.

[0007] Also, another problem with the use of an FIR filter is noiseenhancement. If the transmitted signal picks up noise N_(C) in thechannel, this noise is enhanced by the FIR filter so that the noise Noat the output of the FIR filter is greater than the channel noise N_(C).Also, if the channel noise N_(C) is white, the noise N₀ at the output ofthe FIR filter is non-white, i.e., bursty.

[0008] An example of a frequency domain equalizer 10 is shown in FIG. 3.The frequency domain equalizer 10 includes a Fast Fourier Transform(FFT) module 12 which performs a Fast Fourier Transform on the receivedsignal in order to transform the received signal to the frequencydomain. A multiplier 14 multiplies the frequency domain output of theFFT module 12 by a compensation vector which includes a row ofcoefficients b_(i). An inverse FFT module 16 performs an inverse FFT onthe multiplication results from the multiplier 14 in order to transformthe multiplication results to the time domain.

[0009] It should be noted that, when the frequency domain equalizer 10is used to eliminate ghosts, the frequency domain equalizer 10 must beincluded in every receiver. In order to reduce receiver cost, therefore,it is known to incorporate the inverse FFT module 16 into thetransmitter so that the receivers require only the FFT module 12 and themultiplier 14. A consequence of moving the inverse FFT 16 to thetransmitter is that data is transmitted in many discrete frequencychannels. Accordingly, in the presence of a 100% ghost, the transmitteddata is not recoverable around the null frequencies of FIG. 1.

[0010]FIG. 4 illustrates an exemplary set of coefficients b_(i) whichmay be used by the frequency domain equalizer 10. In order to derive thecoefficients b_(i), an estimator may be used at the output of the FastFourier Transform (FFT) module 12. This estimator models FIG. 1 andinverts this model in order to produce the coefficients b_(i) of FIG. 4.Accordingly, the coefficients b_(i) are chosen so that, when they andthe FFT of the received signal are multiplied by the multiplier 14, thecoefficients b_(i) cancel the ghost. It should be noted that thecoefficients b_(i) should have infinite amplitudes at the frequencieswhere the interference pattern has a zero amplitude. However, thecoefficients b_(i) cannot be made infinite as a practical matter.Accordingly, the coefficients b_(i) are cut off at these frequencies. Anadvantage of cutting off the coefficients b_(i) is that noiseenhancement at the frequencies where the coefficients b_(i) are cut offis materially reduced. Thus, noise enhancement is lower at the output ofthe frequency domain equalizer 10 than would otherwise be the case.However, a disadvantage of cutting off the coefficients b_(i) is thatinformation in the received signal is lost at the cut off frequencies sothat the output of the inverse FFT module 16 becomes only anapproximation of the transmitted data.

[0011] Moreover, it is known to use empty guard intervals between thevectors employed in the frequency domain equalizer 10 of FIG. 3. Theguard intervals are shown in FIG. 5 and are provided so that receivedvectors and ghosts of the received vectors do not overlap because suchan overlap could otherwise cause intersymbol interference. Thus, theguard intervals should be at least as long as the expected ghosts. It isalso known to use cyclic extensions of the vectors in order to give thereceived signal an appearance of periodicity. Accordingly, a FastFourier Transform of the received signal and a Fourier Transform of thereceived signal appear identical.

[0012] The present invention is directed to an equalizer which overcomesone or more of the above noted problems.

SUMMARY OF THE INVENTION

[0013] In accordance with one aspect of the present invention, areceiver receives a signal containing data distributed in both time andfrequency. The receiver comprises a vector transform and a vectoradjuster. The vector transform is arranged to perform a transform on thereceived signal using a plurality of transform vectors. The vectoradjuster is responsive to the transform of the received signal in orderto adjust the transform vectors so that the data can be recovered evenin the presence of a strong ghost.

[0014] In accordance with another aspect of the present invention, areceiver receives a signal containing data distributed in both time andfrequency. The receiver includes a vector transform that is arranged toperform a transform on the received signal using a plurality of receivertransform vectors. The receiver transform vectors are based upon acorresponding plurality of transmitter vectors and channel effects sothat the data can be recovered by the vector transform even in thepresence of a strong ghost.

[0015] In accordance with yet another aspect of the present invention, areceiver receives a signal from a channel. C* designates the channelwith interference. The signal contains data, and the data has beenprocessed by a transmitter transform so that the data is distributed inboth time and frequency. A designates the transmitter transform. Thereceiver includes a receiver transform arranged to perform a transformon the received signal using a plurality of receiver transform vectorsso as to recover the data even in the presence of a strong ghost, and T*designates the receiver transform. The receiver transform vectors arearranged so that the following equation is satisfied: A×C*×T*=I, whereinI is substantially the identity matrix.

[0016] In accordance with yet another aspect of the present invention, acommunication system includes a transmitter and a receiver. Thetransmitter includes a transmitter transform A arranged to randomlydistribute data to be transmitted in both time and frequency, and thetransmitter is arranged to transmit a signal including the distributeddata into a channel. The channel with interference is represented by C*.The receiver is arranged to receive the signal, and the receiverincludes a receiver transform T* arranged to perform a transform on thereceived signal so as to recover the data even in the presence of astrong ghost. The receiver transform is arranged so that the followingequation is satisfied: A×C*×T*=I, and I is substantially the identitymatrix.

[0017] In accordance with a further aspect of the present invention, atransmitter includes a transmitter transform which is arranged torandomly distribute data to be transmitted in both time and frequency.The transmitter is arranged to add a guard interval to the randomlydistributed data. The guard interval is known, is non-empty, and isnon-related to the randomly distributed data. The transmitter isarranged to transmit the randomly distributed data and guard interval.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] These and other features and advantages of the present inventionwill become more apparent from a detailed consideration of the inventionwhen taken in conjunction with the drawings in which:

[0019]FIG. 1 shows an interference pattern which could result when twosignals in the same frequency band are received by a receiver atsubstantially the same time;

[0020]FIG. 2 illustrates the response of an FIR filter which is commonlyused as a time domain equalizer in a receiver in order to eliminateghosts;

[0021]FIG. 3 illustrates a frequency domain equalizer which is used in areceiver in order to eliminate ghosts;

[0022]FIG. 4 illustrates an exemplary set of coefficients b_(i) that areused by the frequency domain equalize of FIG. 3 in order to cancelghosts;

[0023]FIG. 5 illustrates guard intervals which may be used betweentransmitted vectors in systems employing equalizers;

[0024]FIG. 6 illustrates an equalizer which includes a vector domaintransform pair (i.e., a vector domain transform and an inverse vectordomain transform) according to a preferred embodiment of the presentinvention;

[0025]FIG. 7 illustrates one portion of the vector domain transform pairof FIG. 6 in additional detail;

[0026]FIG. 8 illustrates a specific implementation of the portion of thevector domain transform pair illustrated in FIG. 7;

[0027]FIG. 9 illustrates the other portion of the vector domaintransform pair of FIG. 6 in additional detail.

[0028]FIG. 10 illustrates an exemplary correlation result that may beobtained from the equalizer of FIG. 6;

[0029]FIG. 11 illustrates exemplary correlation results that may beobtained during a training session from the equalizer of FIG. 6; and,

[0030]FIG. 12 is a diagrammatical overview of the present invention.

DETAILED DESCRIPTION

[0031] A vector domain equalizer 20 according to one embodiment of thepresent invention is shown in FIG. 6. The vector domain equalizer 20relies on vectors to distribute the transmitted data in both time andfrequency so that the vectors are essentially random in the time andfrequency domains. Accordingly, in a heavily ghosted channel, all datacan be recovered with small noise enhancement, and any enhanced noisethat does exist is near white.

[0032] The vector domain equalizer 20 includes an inverse vector domaintransform 22 and a vector domain transform 24 which are separated by achannel 26. Accordingly, the inverse vector domain transform 22 may bepart of a transmitter, and the vector domain transform 24 may be part ofa receiver. Alternatively, the vector domain transform 24 may be part ofthe transmitter and the inverse vector domain transform 22 may be partof the receiver, so that either portion of a transform pair may be inthe transmitter as long as the receiver has the inverse of the portionthat is in the transmitter. As a still further alternative, as in thecase of the frequency domain equalizer 10 described above, both theinverse vector domain transform 22 and the vector domain transform 24may be in the receiver. Indeed, one of the vector domain transform pair22/24 is referred to as the vector domain transform and the other isreferred to as the inverse vector domain transform only for conveniencein order to merely denote the inverse relationship between the transform22 and the transform 24.

[0033] The inverse vector domain transform 22 of FIG. 6 is shown in moredetail in FIG. 7. A matrix multiplier 30 of the inverse vector domaintransform 22 performs a matrix multiplication between an input datablock 32 and a transform matrix 34. The input data block 32 may includeany number of data elements arranged in a row. These data elements maybe bits, symbols, or any other suitable data entities. The transformmatrix 34 comprises a plurality of vectors arranged in columns, and eachvector of the transform matrix 34 preferably has a length commensuratewith the number of data elements of the input data block 32, althoughthe size of the input data block 32 and the length of the vectors of thetransform matrix 34 need not necessarily be commensurate. Also, thenumber of vectors of the transform matrix 34 should preferably (but notnecessarily) be commensurate with the number of data elements in theinput data block 32. For example, if there 256 data elements in theinput data block 32, the transform matrix 34 should preferably have 256vectors each having 256 elements. The output of the matrix multiplier 30is an output data block 36 having a number of data elements commensuratewith the number of data elements of the input data block 32. Thus, ifthere are 256 data elements in the input data block 32, the output datablock has 256 data elements resulting from the matrix multiplication ofthe 256 element input data block 32 and the 256 element transformvectors of the transform matrix 34.

[0034] Because of the matrix multiplication performed by the matrixmultiplier 30, each data element in the input data block 32 isdistributed to each data element of the output data block 36.Accordingly, if one or more transmitted elements of the output datablock 36 are lost in the channel or cannot be recovered in the receiverdue to a ghost, the data elements of the input data block may berecovered in the receiver from the other (non-lost) transmitted elementsof the received output data block 36. Thus, it should be noted that thevectors stored in the transform matrix 34 may be any vectors which, incombination with the matrix multiplier 30, distribute the data elementsof the input data block 32 randomly throughout the vector domainoccupied by the data elements of the output data block 36.

[0035] A specific example of the inverse vector domain transform 22 isshown in FIG. 8. As shown in FIG. 8, the operations of the matrixmultiplier 30 and the transform matrix 34 are performed by (i) a dotproduct multiplier 42, which performs a dot product multiplicationbetween the input data block 32 and a function S₀, and (ii) a Walshtransform 44, which performs a Walsh transform on the dot productresults from the dot product multiplier 42 in order to produce theoutput data block 36. The function S₀ can be any distributing vectorfunction which has good randomness properties. For example, the functionS₀ may be a Bent function.

[0036] The vector domain transform 24 is shown in more detail in FIG. 9.The vector domain transform 24 includes a transform 50 which correlatesthe received signal with each of a plurality of receiver vectors V_(R).That is, the transform 50 essentially performs a matrix multiplicationbetween the received signal and the vectors V_(R). This matrixmultiplication assumes that the receiver employing the vector domaintransform 24 is synchronized to the received signal. Any suitablesynchronizer may be used to perform this synchronization.

[0037] The data transmitted through the channel 26 is received, forexample, as a row vector. During matrix multiplication, the transform 50multiplies each component of the received row vector by a correspondingcomponent in a first column of the receiver vectors V_(R), and sums themultiplication results to produce a first component r₁ of a vector r_(i)at the output of the transform 50. The transform 50 next multiplies eachcomponent of the received row vector by a corresponding component in asecond column of the receiver vectors V_(R), and sums the multiplicationresults to produce a second component r₂ of the output vector r_(i), andso.

[0038] Before training, the vectors V_(R) applied by the transform 50are substantially identical to the vectors of the transform matrix 34.The vectors applied by the transform 50, however, may have a guardinterval on each side of each vector to provide adequate separationbetween correlations. This guard interval should be known and should notbe related to the transmitted data. For example, the guard intervals maycontain components, such as bits, essentially all having substantiallythe same value, such as zero. Thus, in the present invention, no cyclicextensions of the receiver vectors V_(R) applied by the transform 50 arerequired. After training, the receiver vectors V_(R) applied by thetransform 50 become the receiver vectors V*_(R) which are likely to bedifferent from the vectors of the transform matrix 34.

[0039] Assuming no channel distortion such as may be caused by channelinterference, and assuming that the transform 50 uses the same vectorsas are stored in the transform matrix 34, the matrix multiplicationperformed by the transform 50 produces the input data block 32. Anexemplary component j in the i^(th) vector of the transform output rproduced by the transform 50 under these conditions is shown in FIG. 10,where the output of the transform 50 may be designated r_(i) asdiscussed above, and where the component j in the i^(th) vector of thetransform output r may be designated r_(i) _(j) .

[0040] However, if channel distortion exists, the actual component j inthe i^(th) vector of the transform output r may have the appearance ofFIG. 11, depending upon the amount of channel distortion. Accordingly,this channel distortion may make the input data block 32 impossible torecover. In order to force the actual component j in the i^(th) vectorof the transform output r to have the appearance of FIG. 10 in thepresence of channel distortion, a training session is invoked where thevectors of the transform 50 are adjusted according to channel distortionsuch that, in the presence of channel distortion, the data of the inputdata block 32 is recovered.

[0041] During training, a known data block is transformed by the matrixmultiplier 30 and the transform matrix 34 in order to distribute thedata in the known data block in both time and frequency. The transformof the known data block is transmitted through the channel and is matrixmultiplied by the vectors V_(R) in the transform 50 of the receiver. Forexample, the known data block may be transmitted periodically at knowntimes, such as during the transmission of synchronization information.

[0042] A switch 54 is closed during training in order to pass the outputdata vector r from the transform 50 to a comparator 56. The comparator56 subtracts a reference vector T_(i) from the output data vector r_(i)produced by the transform 50 in order to produce an error vector e_(i).The reference vector T_(i) is the data which is produced by matrixmultiplying the known data block by the vector matrix 34. Thus, thereference vector T_(i) has as many components as there are data elementsin the known data block. Accordingly, the comparator 56 subtracts thefirst component of the reference vector T_(i) from the first dataelement in the output data vector r_(i) from the transform 50 in orderto produce a first error component e_(i) _(j) in the error vector e_(i),the comparator 56 subtracts the second component of the reference vectorT_(i) from the second data element in the output data vector r_(i) fromthe transform 50 in order to produce a second error component e in theerror vector e_(i), and so on. As a result, the error vector e_(i) alsohas as many components as there are data elements in the known datablock.

[0043] Thus, if the vectors applied by the transform 50 have alreadybeen fully adjusted to the point where the effects of channel distortionare effectively nullified, the error vector e_(i) at the output of thecomparator 56 is zero. However, if the vectors stored in the vectormatrix 52 are not fully adjusted so that the effects of channeldistortion are not effectively nullified, the error vector e_(i) at theoutput of the comparator 56 is not zero. For example, the errorcomponent j of the error vector e_(i) may be the difference betweencomponent j of the reference vector T_(i) as shown in FIG. 10 and theoutput r_(i) _(j) from the transform 50 for data element j as shown inFIG. 11.

[0044] Gain (k) is applied by an amplifier 58 to the error vector e_(i)from the comparator 56 in order to produce a gain adjusted error vectorke_(i). This gain is preferably less than one so that the vectorsapplied by the transform 50 are not corrected in one operation, whichcould otherwise lead to instability. The vectors applied by thetransform 50 may be replicated in a memory 60. A multiplier 62multiplies the gain adjusted error vector ke_(i) from the gain block 58and the vectors stored in the memory 60, and a summer 64 adds themultiplication results back to those vectors and stores the adjustedvectors back in the memory 60. Specifically, the multiplier 62multiplies the first component of the gain adjusted error vector ke_(i)from the gain block 58 and the first column of the vectors stored in thememory 60, and the summer 64 adds this multiplication result back tothat first column and stores that adjusted first column in the memory60. Next, the multiplier 62 multiplies the second component of the gainadjusted error vector ke_(i) from the gain block 58 and the secondcolumn of the vectors stored in the memory 60, and the summer 64 addsthis multiplication result back to that second column and stores thatadjusted second column in the memory 60. This operation is repeated foreach of the columns stored in the memory 60. When all columns stored inthe memory 60 have been so adjusted, the vectors stored in the memory 60are loaded into the transform 50 for application to subsequent receivedvectors.

[0045] Because of the gain imposed by the amplifier 58 on the error fromthe comparator 56, several training data blocks must be transmitted inorder for the vectors applied by the transform 50 to properly recoverthe input data at the output of the transform 50. Each training datablock should preferably be different. Once the vectors applied by thetransform 50 reach the fully adjusted state where the error from thecomparator 56 is zero, these vectors have been influenced by channeleffects such that, when they are used by the vector domain equalizer 20,ghosts are substantially eliminated from a received signal.

[0046] In summary, the present invention operates in accordance with thefollowing description. As shown in FIG. 12, data-in to be transmittedare processed in blocks by a first transform A (i.e., the inverse vectordomain transform 22) of a transform pair A/T to produce processed datad1. (Each data block data-in may contain, for example, 256 symbols.) Theprocessed data dl have the property that the original data elements indata-in are distributed evenly and randomly by the first transform Ainto the processed data d1. (This distribution is predefined by thefirst transform A and is known.) The processed data d1 are thentransmitted through the channel C and arrive at the receiver as receiveddata d2. The received data d2 are processed by a second transform T(i.e., the vector domain transform 24) of the transform pair A/T toproduce output data-out. The second transform T is the inverse of thefirst transform A under ideal channel conditions where d1=d2 and C isequal to the identity matrix I. Accordingly, A×C×T=I, where x denotesmatrix multiplication. After the received data d2 is processed by thesecond transform T, the original information data-in are restored sothat data-in=data-out. When there is interference in the channel C suchthat the channel becomes C*, A×C*×T≠I and, therefore, data-out≠data-in.However, after a minimizing process such as the training protocoldescribed above, the second transform T becomes T* so that A×C*×T*=Iand, therefore, data-out=data-in. Thus, all information in data-in isrecovered. It should be noted that, as the second transform T ismodified into T*, some noise enhancement results. However, in this case,the enhanced noise is near white when viewed at data-out because of theeven/random distribution/redistribution of data.

[0047] Certain modifications of the present invention have beendiscussed above. Other modifications will occur to those practicing inthe art of the present invention. For example, a particular transformpair is illustrated in FIGS. 5-8. However, it should be understood thatany other transform pair may be used in connection with the presentinvention as long as the data to be transmitted are distributedsubstantially uniformly in both time and frequency.

[0048] Moreover, because the present invention operates mostsatisfactorily in the presence of ghosts and other linear distortions,the term ghost as used herein in connection with the present inventionincludes ghosts and/or other linear distortions.

[0049] Furthermore, as described above, the transform 50 is modifiedthrough training so that, in the presence of channel interference andchanging channel interference, the data recovered by the transform 50 isthe same as the input data 32. However, the transform 50 may be modifiedby processes other than training.

[0050] Accordingly, the description of the present invention is to beconstrued as illustrative only and is for the purpose of teaching thoseskilled in the art the best mode of carrying out the invention. Thedetails may be varied substantially without departing from the spirit ofthe invention, and the exclusive use of all modifications which arewithin the scope of the appended claims is reserved.

What is claimed is:
 1. A receiver, wherein the receiver receives asignal containing data distributed in both time and frequency, thereceiver comprising: a vector transform arranged to perform a transformon the received signal using a plurality of transform vectors; and, avector adjuster responsive to the transform of the received signal inorder to adjust the transform vectors so that the data can be recoveredeven in the presence of a strong ghost.
 2. The receiver of claim 1wherein the vector adjuster comprises a comparator arranged to comparethe transform to a reference.
 3. The receiver of claim 2 wherein thereference is a known block of data stored in the receiver.
 4. Thereceiver of claim 3 wherein the reference is stored in a transmitter andis used to form a training signal that is used by the vector adjuster toadjust the transform vectors.
 5. The receiver of claim 2 wherein thevector adjuster comprises a vector modifier arranged to modify thetransform vectors in response to the comparator so that the transformvectors are modified to compensate for channel interference.
 6. Thereceiver of claim 2 wherein the comparator produces comparison results,and wherein the vector adjuster comprises a gain block arranged toimpose a fractional gain on the comparison results.
 7. The receiver ofclaim 6 wherein the vector adjuster comprises a vector modifier arrangedto modify the transform vectors in response to the comparator so thatthe transform vectors are modified to compensate for channelinterference.
 8. The receiver of claim 6 wherein the vector adjustercomprises a multiplier arranged to multiply an output of the gain blockand the transform vectors.
 9. The receiver of claim 8 wherein themultiplier produces multiplication results, and wherein the vectormodifier comprises a summer arranged to sum the multiplication resultsand the transform vectors in order to adjust the transform vectors. 10.The receiver of claim 1 further comprising a switch arranged tointerconnect the vector transform and the vector adjuster during vectoradjustment.
 11. The receiver of claim 1 wherein the vector transformperforms a matrix multiplication of the received signal and thetransform vectors.
 12. The receiver of claim 1 wherein the vectoradjuster is arranged to adjust the transform vectors in accordance withchannel interference.
 13. A receiver, wherein the receiver receives asignal containing data distributed in both time and frequency, whereinthe receiver includes a vector transform arranged to perform a transformon the received signal using a plurality of receiver transform vectors,and wherein the receiver transform vectors are based upon acorresponding plurality of transmitter vectors and channel effects sothat the data can be recovered by the vector transform even in thepresence of a strong ghost.
 14. The receiver of claim 13 wherein thereceiver transform vectors are the transmitter vectors modifiedaccording to channel effects.
 15. The receiver of claim 13 wherein thereceiver comprises a comparator arranged to compare the transform to areference.
 16. The receiver of claim 15 wherein the reference is a knownblock of data stored in the receiver.
 17. The receiver of claim 16wherein the reference is stored in a transmitter and is used to form atraining signal that is used by the receiver to adjust the receivertransform vectors.
 18. The receiver of claim 15 wherein the receiverfurther comprises a vector adjuster arranged to adjust the transformvectors in response to the comparator so that the receiver transformvectors are modified to compensate for channel interference.
 19. Thereceiver of claim 15 wherein the comparator produces comparison results,and wherein the receiver further comprises a gain block arranged toimpose a fractional gain on the comparison results.
 20. The receiver ofclaim 19 wherein the receiver further comprises a vector adjusterarranged to adjust the transform vectors in response to the comparatorso that the receiver transform vectors are modified to compensate forchannel interference.
 21. The receiver of claim 19 wherein the receiverfurther comprises a multiplier arranged to multiply an output of thegain block and the transform vectors.
 22. The receiver of claim 21wherein the multiplier produces multiplication results, and wherein thereceiver further comprises a summer arranged to sum the multiplicationresults and the transform vectors in order to adjust the transformvectors.
 23. The receiver of claim 22 further comprising a switcharranged to interconnect the vector transform and the vector adjusterduring vector adjustment.
 24. The receiver of claim 13 wherein thevector transform performs a matrix multiplication of the received signaland the receiver transform vectors.
 25. A receiver, wherein the receiverreceives a signal from a channel, wherein C* designates the channel withinterference, wherein the signal contains data, wherein the data hasbeen processed by a transmitter transform so that the data isdistributed in both time and frequency, wherein A designates thetransmitter transform, wherein the receiver includes a receivertransform arranged to perform a transform on the received signal using aplurality of receiver transform vectors so as to recover the data evenin the presence of a strong ghost, wherein T′ designates the receivertransform, wherein the receiver transform vectors are arranged so thatthe following equation is satisfied: A×C*×T*=I and wherein I issubstantially the identity matrix.
 26. The receiver of claim 25 whereinC designates the channel without channel interference, wherein Tdesignates the receiver transform if channel interference is not presentin the channel, wherein T′ designates the receiver transform if channelinterference is present in the channel, and wherein the receivertransform satisfies the following equation with no channel interference:A×C×T=I.
 27. The receiver of claim 26 wherein C=I.
 28. The receiver ofclaim 26 wherein the receiver comprises an adjuster, and wherein theadjuster is arranged to adjust the receiver transform vectors inresponse to the channel interference in order to produce the receivertransform T′.
 29. The receiver of claim 28 wherein the adjustercomprises a comparator arranged to compare the transform to a reference.30. The receiver of claim 29 wherein the reference is a known block ofdata stored in the receiver.
 31. The receiver of claim 30 wherein thereference is stored in a transmitter and is used to form a trainingsignal that is used by the vector adjuster to adjust the transformvectors.
 32. The receiver of claim 29 wherein the comparator producescomparison results, and wherein the adjuster further comprises a gainblock arranged to impose a fractional gain on the comparison results.33. The receiver of claim 32 wherein the adjuster further comprises amultiplier arranged to multiply an output of the gain block and thereceiver transform vectors.
 34. The receiver of claim 33 wherein themultiplier produces multiplication results, and wherein the adjusterfurther comprises a summer arranged to sum the multiplication resultsand the receiver transform vectors in order to produce the receivertransform T′.
 35. The receiver of claim 34 further comprising a switcharranged to interconnect the receiver transform and the adjuster duringvector adjustment.
 36. The receiver of claim 25 wherein the receivertransform performs a matrix multiplication of the received signal andthe receiver transform vectors.
 37. The receiver of claim 25 wherein Cdesignates the channel without interference, wherein T designates thereceiver transform without channel interference, and wherein T=A⁻¹ whenthere is substantially no channel interference.
 38. A communicationsystem including a transmitter and a receiver, wherein the transmitterincludes a transmitter transform arranged to randomly distribute data tobe transmitted in both time and frequency, wherein A designates thetransmitter transform, wherein the transmitter is arranged to transmit asignal including the distributed data into a channel, wherein C*designates the channel with interference, wherein the receiver isarranged to receive the signal, wherein the receiver includes a receivertransform arranged to perform a transform on the received signal so asto recover the data even in the presence of a strong ghost, wherein T′designates the receiver transform, wherein the receiver transform isarranged so that the following equation is satisfied: A×C*×T*=I andwherein I is substantially the identity matrix.
 39. The communicationsystem of claim 38 wherein C designates the channel without channelinterference, wherein T designates the receiver transform withoutchannel interference, wherein T′ designates the receiver transform withchannel interference, and wherein the receiver satisfies the followingequation with no channel interference: A×C×T=I.
 40. The communicationsystem of claim 39 wherein C=I.
 41. The communication system of claim 38wherein the receiver transform performs a matrix multiplication of thereceived signal and the receiver transform vectors.
 42. A transmitter,wherein the transmitter includes a transmitter transform arranged torandomly distribute data to be transmitted in both time and frequency,wherein the transmitter is arranged to add a guard interval to therandomly distributed data, wherein the guard interval is known, isnon-empty, and is non-related to the randomly distributed data, andwherein the transmitter is arranged to transmit the randomly distributeddata and the guard interval.
 43. The transmitter of claim 42 wherein theguard interval comprises components, and wherein the components aresubstantially equal.
 44. The transmitter of claim 42 wherein the guardinterval comprises essentially all zeros components.